Yeah, this whole thing about Briggs and the body seems very important....'there's a body alright' indicates that something is definitely dead(everything is not alright) and also a mystery to solve...

Going by the 'facts' alone is not going to get there, there are too many contradictions and impossibilities, ending up like Andy and Hawk looking over papers again and again for an Indian.  Hawk finally found a clue by sheer intuition alone, almost like the original cooper throwing rocks or matches, and also Cole(Cooper's mentor) trained Cooper this way and told his new agent 'look for the spiritual base on the left finger/hand/arm'...... so there is something more of a 'spiritual' method going on here, which seems to be association with intuition and feeling primarily intended by the creators.  I do not think feeling and intuition alone will do the trick and that the 'spiritual' can be explained in thinking and language, but this fails, leads to new clues, etc....

The 'concept' of Brigs reappearing in multiple bodies throughout the years seems to fit with cooper being in two bodies at once and multiple people in different locations having the same body etc., and that this can be repeated, so that people who access the lodge are sort of trapped in a state of deadlock of thinking and reality(we think or try something, hit an obstacle, cannot pass because of some crap in reality), failure, where desire falls apart, thus the red-desire curtains lead you to fall apart in the face of unsolvable sexual antagonism.  Now this show has it set up where the characters in the lodge are sort of failed ghosts who became disembodied, but held in limbo and come back to haunt because the debt the world owes their unsolved injustice has not been payed/solved, they are then re-materialized in order to attempt again solving it, only to be thrown back into hell if the world fails in solving it, making no progress, and repeating the same deadlock, time and time again...BOB, BOB, BOB, BOB(and Laura) etc..  Thus Briggs has re-materialized so many times and different places because of the worlds failure to solve his problem...

Briggs stood for an old fashioned male authority figure, for law, community, non-tyrannous government, and a solid home life with reliable wife who knew the value of 'home'.  While figures like Laura/BOB tore this to shreds and have 'time and time again' repeatedly enforced their tyranny on the world, thus now there are many more 'lauras' in twin peaks, waiting for the Jean Michel's orders. 

Briggs would have deep troubles with this antagonism, thus he tried to swallow Dougie's closed 'wedding ring' and thats all he ate, he only wants to recover the lost enjoyment he got within the old configuration of paternal law and private affections of home, but this has been usurped by feminine autority of Laura-Mother.  Briggs is trying to keep alive his old desire, but the world has changed since and old Twin Peaks/World is gone, thus he does not find it, but something else. 

  Now, Briggs body was with the head of a woman, as if he is thinking like a woman, while his male head is in outer space saying 'blue rose'(and Cooper has also hit this problem after encountering Laura/twin peaks), meaning an unsolvable sexual antagonism that he cannot solve with his desire. This leads to Hastings in prison, with the head of his 'burned-hobo'(got to close to the 'fire' and ruined himself).  This burned hobo also appears around Briggs body, spelling trouble for Briggs, that he encountered an antagonism similar to hastings, a sexual antagonism and the failure of desire. 

     Now we know the red/room-lodge is sort of a 'waiting ground' for the spiritual that reflects the real world antagonisms in their disjointed-failed apparitions, which then materializes 'ghosts' in different places as embodiments of those spiritual antagonisms when they become relevant in the world again.  The same antagonism materializes in different places all over the world, and people's interactions create and reinforce the authority of how to deal with these situations.  Thus all of the 'case files' of the couples are about man and woman abusing each other, leading to killings, brutal cruelty, etc.  These are all variations of the same sexual antagonism, the 'blue rose'. The common theme in most of these cases are the woman leading, motherly authority, manipulating the man and his law-rules, tearing him apart as he looks to her for affection, all variations on the mystery of Laura Palmer, the seductive girl controlling the towns affections, driving the father crazy, etc. (Beverly being brutally cruel to her dying husband and asserting her cheating, Hastings wife aggravating her husband into self destruction).

   Briggs has the head of a woman, thinking like a woman, following womans authority, while the apparition that killed the kids in new york was a female body with a male head (woman thinking like a man, controlling the law, public life, etc.) Tyrannous feminine authority sees what the law lacks, that it needs the exception of the woman where law and normality dissolve in desire, one thing is elevated, not treated as the same, transcends the law of how you justly deal with people on a normal basis, etc. changing things around, which then settles down in home life...feminine authority capitalizes on this need of the man, who is then forced to chase after the affections and tortured in the process by the whims of a 'woman's intuition', their arbitrary games etc., which seems monstrous to a male who's spiritual existence depends on them and who, like Briggs, is in the world dealing with law, justice, etc. and not arbitrariness.  There are other ways of dealing with this antagonism and the female authority, for example one can complement it perfectly by responding to the feminine domination with masochistic acceptance(impotence), then desiring this and showing that they are the strongest(omnipotent), and like the female tyranny whose rules they have accepted, only care about personal affections at expense of the law, something like a businessman controlling a state-government.   Mr. C, Red, Richard Horne are these types of figures, people who impose on the public an excess of the law, making it their own personal property-profits and feelings(capitalisims admonitory feminine law that everything services profit, not the justice-law concerns that are universal to all people; and its state, something like terrorism laws, called Patriot Act here in the US that suspends all human rights whenever they want, the government surveillance, Assange, etc.).  Dougie represents another way to respond to this.   

      What about Dougie and his connection to Briggs? Dougie was also led around by women, and was about to be burned(by mafia), but reacted to the female authority in a more 'impotent' than 'omnipotent' way, just giving away all his money following Jade, chasing desire and womans lead; but notice he still accepts the law of the game, that chasing arbitrary affections, profits-gold, etc., is all there is to think about, like it is God.  Dougie and Briggs are connected here, and in the failure of home life as paternal authority, failure to be a good father, have a solid home/wife, etc.  Briggs hit the 'blue rose' antagonism and has been out on a spree chasing lost affection/enjoyment like both Dougie and Hastings.  Briggs swallowed the ring, took his failure hard, and like Hastings, tried to fix it by 'evening the score' or doing what the woman did, chasing arbitrarily down a 'lost highway', hoping the problem will somehow disappear.

     We know the military found Briggs prints many time, and the military investigator says in the morgue that usually his prints are found at crime scenes, indicating that he was in a similar situation to Hastings, but this time there is a body, the antagonism has reached a turning point as Cooper is trying at it in a different way(still absent from twin peaks as a town, which is hiding from the problem, from Laura).  Sleazy dougie disappeared, purpose served, there is a body, hastings in prison, dying guy's emotions were brutalized(knew his wife was cheating and going to die without consolation of even slightest care from wife, so wife can have fun).  Thus, from all of these case files, we switch to cleaning up the scene of the crime, sweeping up the roadhouse(where people come for desire/infinite) like norman bates driven by the tyrannous rule of laura-mother.  A norman bates who then dominates the RR diner(red room diner) a little bit later.......

Who says Briggs 'swallowed' the ring? He might have had it 'force-fed'. (Constance says it's the only thing he 'ate' for days). Think of the movie 'Seven' here. We cannot rule out that Mr. C-from-Rio has some sadistic features....

could be that he was force fed the ring, but this could also still fit with what I said, with more of an emphasis of the whole trouble being forced on briggs by Mr. C; maybe it could just be that he is being continually framed and killed by forces he is trying to stop, trapped in a repetitive non-productive cycle of impotence imposed by a world ruled by Mr. C and people like him..... definitely a possibility, but this would be a failure to change the world from the tryanny of Mr. C/Laura

but I dont think briggs is guaranteed to be so innocent, its open at this point, since every time the military found his prints before they were at a crime scene, indicating his similarity to bill hasting's situation(who it seems like he committed the murder, doesnt remember, like the guy from lost highway, thought it was a dream, blacked out, etc., hides from his failure as a man because of the promiscuous wife by becoming potent young kid, hits the same problem, etc.)

briggs originally died in a fire after meeting Mr. C back in original twin peaks,  which also links up with the tyrannical mother who killed her husband in 'wild at heart', which was written at the same time as original twin peaks, and laura palmer.   thus the scorched-hobo, like hastings and his burnt-hobo who got too close to a 'fire'/blue rose, standing in the way of Laura and her men....